Coherent Control of the Exciton-Biexciton System in an InAs Self-Assembled Quantum Dot Ensemble

Coherent control of a strongly inhomogeneously broadened system, namely, InAs self-assembled quantum dots, is demonstrated. To circumvent the deleterious effects of the inhomogeneous broadening, which usually masks the results of coherent manipulation, we use prepulse two-dimensional coherent spectroscopy to provide a size-selective readout of the ground, exciton, and biexciton states. The dependence on the timing of the prepulse is due to the dynamics of the coherently generated populations. To further validate the results, we performed prepulse polarization dependent measurements and confirmed the behavior expected from selection rules. All measured spectra can be excellently reproduced by solving the optical Bloch equations for a 4-level system.

Figure 1

(a) Schematics of the prepulse 2DCS experiment for an InAs QD ensemble and time ordering. Delays between the prepulse, $A^{*}$, $B$, $C$, and the signal are denoted as $\mathrm{\Delta }t$, $\tau$, $T$, $t$, respectively. (b) The energy level diagram showing the ground ($|G⟩$), horizontal ($|H⟩$) and vertical ($|V⟩$) excitons, and biexciton ($|B⟩$) states. The coherent paths for the interaction with the prepulse are shown as solid arrows and the radiative decay paths are shown as dashed arrows. (c)–(f) Double-sided Feynman diagrams representing all the quantum pathways [24] for cross-linear polarization, where (c), (d), (e), and (f) start with population in the ground, H exciton, and biexciton states, respectively. The vertical lines represent evolution of the density matrix. The arrows in each diagram from the bottom to the top correspond to pulses $A^{*}$, $B$, $C$, and the signal, respectively.

Figure 2

2D rephasing amplitude spectra using prepulse power of (a) 0, (b) 45, and (c) 94 mW. Color corresponds to amplitude in the figures. The delay between the prepulse and 2DCS probe is 15 ps. The polarization for the prepulse is horizontal and for 2DCS is cross-linear ($H\text{−}HVVH$). The trion (Tr), lower peak (LP), and upper peak (UP) are indicated. The inset in (b) shows a spectrum for the prepulse and each beam in 2DCS, and the arrows in (b) show resonant energy positions for the LP and UP, respectively.

Figure 3

(a) Peak amplitudes of H prepulse 2D rephasing spectra ($H\text{−}HVVH$) for the LP (red circles) and UP (blue squares). Solid lines are simulation results of $|{\rho }_G-{\rho }_H|$ (red) and $|{\rho }_H-{\rho }_B|$ (blue). The bottom axes are for data, whereas the top axes are for simulation results. (b) Simulation results for population in each state, ${\rho }_G$ (solid line), ${\rho }_H$ (dashed line), ${\rho }_V$ (dotted line), and ${\rho }_{\mathrm{B}}$ (dot-dashed line).

Figure 4

(a) Vertically polarized prepulse 2D rephasing amplitude spectra ($V\text{−}HVVH$) at prepulse power of (a) 40 and (b) 126 mW at $\mathrm{\Delta }t=15\mathrm{ps}$. (c) Peak amplitudes of $V\text{−}HVVH$ for the LP (red circles) and UP (blue squares). Solid lines are simulation results of $|{\rho }_G-{\rho }_H|$ and $|{\rho }_H-{\rho }_B|$. The bottom axes are for data, whereas the top axes are for simulation results. (d) Simulation results for the population in each state, ${\rho }_G$ (solid line), ${\rho }_H$ (dashed line), ${\rho }_V$ (dotted line), and ${\rho }_B$ (dot-dashed line).